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Tension or Temperature. Dogs may shake as a way of relieving tension. If a dog is feeling nervous or uncomfortable in a situation, it might shake the whole body as a way of shaking out tension. This behavior also may function as a means of getting attention from other dogs or people.
Muscle Weakness. Dog back legs shaking may also be a sign of muscle weakness. This can for example happen after exercising (leading to overexertion of the hind legs), when you take your dog for a walk, or when the dog leans down to drink water or eat.